Control device, control method, quantum measurement system, and program

Abstract

To improve performance for suppressing a quantum error.SOLUTION: A control device comprises: a quantum state calculation part for calculating a plurality of quantum states including a quantum state which has been influenced by a quantum error being a suppression object; a quantum measurement control part for measuring a matrix indicating Hamiltonian on a partial space which is defined by a positive semidefinite operator related to the plurality of quantum states, and an overlap matrix of the partial space with the positive semidefinite operator set as an identity operator, or brought into the quantum state influenced by the quantum error; an error suppression calculation part for calculating the peculiar energy of the Hamiltonian which is suppressed in the quantum error as a peculiar value of a generalized peculiar equation indicating the Hamiltonian; and a quantum error suppression part for calculating an expectation value of a physical amount from an objective physical amount of a quantum measurement on the basis of the calculated peculiar energy of the Hamiltonian.SELECTED DRAWING: Figure 5

Description

[Technical Field]

[0001] The present invention relates to a control device, a control method, a quantum measurement system, and a program. [Background technology]

[0002] Quantum computers are a technology that performs calculations by utilizing the principle of superposition in quantum mechanics, and are expected to be able to quickly solve problems such as prime factorization and quantum chemistry calculations, so their development is being actively pursued around the world. The qubits handled by quantum computers can produce errors that cause deviations in the "superposition" ratio of 0 and 1, in addition to errors that occur in classical computers, such as swapping 0 and 1. Therefore, methods for suppressing the errors that occur in quantum computers (quantum errors) are being researched. Conventional methods for suppressing quantum errors are divided into two types: methods that require information about the quantum error to be suppressed, and methods that do not require information about the quantum error.

[0003] Conventionally, virtual distillation (Non-Patent Document 1, Non-Patent Document 2) and subspace expansion (Non-Patent Document 3) have been disclosed as representative quantum error suppression mechanisms that do not require information about quantum errors. Virtual distillation is a method in which multiple copies of the same quantum state that has been subjected to a quantum error are prepared, and measurements are taken after quantum entanglement operations are performed between the copies, and the results are processed using a classical computer. In virtual distillation, the accuracy of quantum error suppression improves as the number of copies of the quantum state increases.

[0004] The subspace expansion method measures the Pauli operator (and the product of Pauli operators) for a quantum state affected by quantum errors, and processes the measurement results using a classical computer. The virtual distillation method performs entangled measurements on a copy of the quantum state, transferring the quantum state to a space with exchange symmetry and no quantum errors, thereby suppressing quantum errors. By representing the quantum state using both a classical computer and a quantum computer, the subspace expansion method can expand the range of quantum states that can be represented compared to when represented using a quantum computer alone, thereby reducing quantum errors. [Advanced Technology Documents]

Non-licensed literature

[0005] [Non-licensed document 1] McClean, Jarrod R., et al. "Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states." Physical Review A 95.4 (2017): 042308. [Non-licensed document 2] Koczor, Balint. "Exponential error suppression for near-term quantum devices." Physical Review X 11.3 (2021): 031057. [Non-licensed document 3] Huggins, William J., et al. "Virtual distillation for quantum error mitigation." Physical Review X 11.4 (2021): 041036.

Non-licensed Document 4

Non-licensed Document 5

[0006] While the virtual distillation method can suppress probabilistic quantum errors such as bit flips and phase inversions, it cannot prevent the effects of coherent errors such as deviations in the rotation angle of quantum gates. Furthermore, the number of quantum bits that can be realized in quantum computers is limited, which limits the number of copies of quantum states that can be used, limiting the performance of quantum error suppression. Furthermore, while the subspace expansion method is effective in suppressing coherent errors, it is not suitable for suppressing probabilistic quantum errors.

[0007] The disclosed technique aims to improve the performance of quantum error suppression. [Means for solving the problem]

[0008] The disclosed technology is a control device that includes a quantum state calculation unit that calculates multiple quantum states including a quantum state affected by a quantum error that is to be suppressed; a quantum measurement control unit that measures a matrix representing a Hamiltonian on a subspace defined by a positive semidefinite operator related to the multiple quantum states and an overlap matrix of the subspace, with the positive semidefinite operator being an identity operator or a quantum state affected by the quantum error; an error suppression calculation unit that calculates the eigenenergy of the Hamiltonian in which the quantum error has been suppressed as an eigenvalue of a generalized eigenequation that represents the Hamiltonian; and a quantum error suppression unit that calculates the expected value of a physical quantity from a physical quantity that is the subject of quantum measurement based on the calculated eigenenergy of the Hamiltonian. [Effects of the Invention]

[0009] According to the disclosed technology, it is possible to improve the performance of quantum error suppression. [Brief explanation of the drawings]

[0010] [Figure 1]FIG. 1 is a diagram illustrating an example of a system configuration of a quantum measurement system. [Figure 2] FIG. 2 is a diagram illustrating an example of the hardware configuration of a first quantum computer. [Figure 3] FIG. 2 is a diagram illustrating an example of the hardware configuration of a second quantum computer. [Figure 4] FIG. 2 illustrates an example of a hardware configuration of a computer. [Figure 5] FIG. 2 is a diagram illustrating an example of a functional configuration of a control device. [Figure 6] 10 is a flowchart illustrating an example of the flow of a quantum measurement process. DETAILED DESCRIPTION OF THE INVENTION

[0011] Hereinafter, an embodiment of the present invention (the present embodiment) will be described with reference to the drawings. The embodiment described below is merely an example, and the embodiment to which the present invention is applied is not limited to the following embodiment.

[0012] (Outline of this embodiment) The quantum measurement system according to this embodiment is a system for performing quantum measurement with quantum error suppression. The quantum error suppression method is a generalized subspace expansion method that includes the virtual distillation method and the subspace expansion method as special cases.

[0013] In the subspace expansion method, the Pauli operators and their products are measured for quantum states with quantum errors, and the range of quantum states that can be expressed is expanded by processing the results using a classical computer. In contrast, in this embodiment, in addition to measuring the Pauli operators, classical processing similar to the subspace expansion method is also performed on results obtained by measuring the quantum entanglement of multiple quantum states.

[0014] In addition, a simple combination of the subspace expansion method and the virtual distillation method is also included in the generalized subspace expansion method. Since the subspace expansion method can efficiently suppress coherent errors and the virtual distillation method can efficiently suppress stochastic errors, the generalized subspace expansion method can efficiently suppress both coherent errors and stochastic errors.

[0015] Furthermore, while virtual distillation uses copies of "identical" quantum states, generalized subspace expansion can use "non-identical" quantum states or operations other than quantum entanglement. This significantly mitigates the problem of virtual distillation, where the accuracy of quantum error suppression is limited by the number of copies of the quantum state that can be used. Therefore, it enables higher quality error suppression than simply combining subspace expansion and virtual distillation.

[0016] Furthermore, the "power subspace method" and "error subspace method" are particularly useful cases of the generalized subspace expansion method. In the "power subspace method," an ideal quantum state can be expressed as a series expansion of a quantum state affected by a quantum error, thereby achieving calculations with higher accuracy than the virtual distillation method, whose accuracy is limited by the number of copies. In addition, the "error subspace method" uses a quantum state with increased quantum error, thereby achieving error suppression that incorporates the advantages of the extrapolation method of quantum error suppression (Non-Patent Document 4), and achieving calculations with higher accuracy than the virtual distillation method, whose accuracy is limited by the number of copies.

[0017] Hereinafter, examples 1 and 2 will be described as specific examples of this embodiment.

[0018] Example 1 In this embodiment, an example will be described in which quantum errors are suppressed by applying the "power subspace method" as the generalized subspace expansion method.

[0019] Specifically, we explain the procedure for suppressing quantum errors in the eigenstates of a given quantum system Hamiltonian H. The power subspace method is a method for expressing an ideal error-free quantum state as a series expansion of a quantum state with errors.

[0020] 1 is a diagram showing an example of the system configuration of a quantum measurement system. The quantum measurement system 1 includes a control device 10, a first quantum computer 20, and a second quantum computer 30. The control device 10 and the first quantum computer 20 are communicatively connected via a communication line 40. The control device 10 and the second quantum computer 30 are communicatively connected via a communication line 50.

[0021] The control device 10 is a device configured with a classical computer. A classical computer is a computer that performs electronic calculations using electronic circuits. Hereinafter, a classical computer will also be referred to simply as a computer.

[0022] The control device 10 transmits a quantum measurement instruction signal to the first quantum computer 20 via the communication line 40 and receives data indicating the result of the quantum measurement. The control device 10 then calculates the eigenenergy of the Hamiltonian with the quantum error suppressed by solving a generalized eigenequation based on the received data.

[0023] Next, the control device 10 transmits an instruction signal for quantum measurement of the physical quantity to be measured to the second quantum computer 30 via the communication line 50, and receives data indicating the result of the quantum measurement. The control device 10 then applies the eigenenergy of the Hamiltonian in which quantum errors are suppressed to the received data to calculate the physical quantity in which quantum errors are suppressed.

[0024] The first quantum computer 20 and the second quantum computer 30 are devices configured with quantum computers. A quantum computer is a device that performs measurements using quantum mechanical phenomena such as superposition and quantum entanglement.

[0025] The first quantum computer 20 receives a quantum measurement instruction signal from the control device 10 and performs quantum measurements. For example, the first quantum computer 20 calculates multiple quantum states and applies the "power subspace method" to perform quantum measurements for each quantum state as well as quantum measurements for the entanglement of the multiple quantum states. The first quantum computer 20 then transmits data indicating the measurement results, including the Hamiltonian, overlap matrix, etc. of the quantum system, to the control device 10.

[0026] The second quantum computer 30 receives a quantum measurement instruction signal from the control device 10 and performs quantum measurement of the physical quantity of the measurement target. The second quantum computer 30 transmits data indicating the measurement result to the control device 10.

[0027] Note that if the physical quantity to be measured is energy, the quantum measurement system 1 may not include the second quantum computer 30. In this case, the eigenenergy of the Hamiltonian with suppressed quantum errors calculated by the control device 10 corresponds to the physical quantity to be measured. Even if the physical quantity to be measured is not energy, the first quantum computer 20 and the second quantum computer 30 may be implemented by the same hardware. For example, a single quantum computer may function as either the first quantum computer 20 or the second quantum computer 30 by selectively using a setting to function as the first quantum computer 20 and a setting to function as the second quantum computer 30.

[0028] 2 is a diagram showing an example of the hardware configuration of a first quantum computer 20. The first quantum computer 20 includes a first quantum circuit 21, a second quantum circuit 22, and a quantum measurement circuit 23.

[0029] The first quantum circuit 21 and the second quantum circuit 22 are quantum circuits corresponding to each quantum state. Although Fig. 2 shows an example in which there are two quantum states and two corresponding quantum circuits, there may be three or more.

[0030] The quantum measurement circuit 23 is a quantum circuit for performing measurements including quantum entanglement of multiple quantum states by applying the "power subspace method."

[0031] 3 is a diagram showing an example of the hardware configuration of the second quantum computer 30. The second quantum computer 30 includes a quantum measurement circuit 31. The quantum measurement circuit 31 is a quantum circuit for measuring the physical quantity of a measurement target.

[0032] The control device 10 is realized, for example, by the hardware configuration of a computer 500 shown in Fig. 4. The computer 500 shown in Fig. 4 includes an input device 501, a display device 502, an external I / F 503, a communication I / F 504, a processor 505, and a memory device 506. Each of these pieces of hardware is connected to each other via a bus 507 so as to be able to communicate with each other.

[0033] The input device 501 is, for example, a keyboard, a mouse, a touch panel, etc. The display device 502 is, for example, a display, etc. Note that the computer 500 does not necessarily have to have at least one of the input device 501 and the display device 502.

[0034] The external I / F 503 is an interface with an external device such as a recording medium 503a. Examples of the recording medium 503a include a CD (Compact Disc), a DVD (Digital Versatile Disk), an SD memory card (Secure Digital memory card), and a USB (Universal Serial Bus) memory card.

[0035] The communication I / F 504 is an interface for performing data communication with other devices, equipment, systems, etc. The processor 505 is, for example, various types of arithmetic devices such as a CPU, etc. The memory device 506 is, for example, various types of storage devices such as an HDD, SSD, RAM (Random Access Memory), ROM (Read Only Memory), flash memory, etc.

[0036] The control device 10 can realize various processes described below by having the hardware configuration of a computer 500 shown in Fig. 4. Note that the hardware configuration of the computer 500 shown in Fig. 4 is an example, and the computer 500 may have other hardware configurations. For example, the computer 500 may have multiple processors 505 or multiple memory devices 506.

[0037] 5 is a diagram showing an example of the functional configuration of the control device 10. The control device 10 includes a quantum state calculation unit 11, a quantum measurement control unit 12, an error suppression calculation unit 13, and a quantum error suppression unit 14.

[0038] The quantum state calculation unit 11 controls the first quantum computer 20 to calculate a quantum state. For example, the quantum state calculation unit 11 calculates a quantum state that approximates the ground state of a Hamiltonian using a variational quantum eigensolver (VQE) or the like (e.g., Non-Patent Document 5) that operates on the first quantum computer 20. Here, the quantum state calculation unit 11 may calculate a quantum state that is "identical" to an existing quantum state (a copy of the existing quantum state), as in the virtual distillation method, or may calculate a quantum state that is "not identical" to an existing quantum state. The calculated quantum state may be realized by, for example, the first quantum circuit 21, the second quantum circuit 22, etc.

[0039] The quantum measurement control unit 12 uses the calculated quantum state to control quantum measurements by the first quantum computer 20. For example, the quantum measurement control unit 12 may control measurements for quantum entanglement of multiple quantum states, or may control measurements other than quantum entanglement. The quantum measurements are realized by the quantum measurement circuit 23. In this embodiment, the quantum measurement control unit 12 controls the quantum measurements using the power subspace method.

[0040] The error suppression calculation unit 13 performs calculations to suppress errors using the results of the quantum measurements. For example, the error suppression calculation unit 13 calculates the eigenenergy of a Hamiltonian in which quantum errors are suppressed by solving a generalized eigenequation.

[0041] The quantum error suppression unit 14 controls the second quantum computer 30 to perform quantum measurement of the physical quantity of the measurement target, and suppresses quantum errors by applying the error suppression calculation results to the measurement results.

[0042] Next, the operation of the quantum measurement system 1 will be described. Here, the meaning of each symbol in the following description will be explained. H is a matrix representing the Hamiltonian of the quantum system. ρ is a quantum state affected by a quantum error to which error suppression is applied. σ i is a general operator associated with the quantum state to which we wish to apply error suppression. σ i † is σ i A is a general positive semidefinite operator associated with the quantum state to which we want to apply error suppression. We can also set A=I (identity operator). Also,

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[0047] 6 is a flowchart showing an example of the flow of quantum measurement processing. The quantum state calculation unit 11 calculates a quantum state (step S101). Specifically, the quantum state calculation unit 11 calculates a quantum state that approximates the ground state of the Hamiltonian using a variational quantum eigensolver operating in the first quantum computer 20. When determining an excited state, the quantum state calculation unit 11 calculates an approximation of the excited state using a subspace-search variational quantum eigensolver (SSVQE) or the like. The quantum state obtained here is hereinafter referred to as ρ.

[0048] Next, the quantum measurement control unit 12 controls the quantum measurement (step S102). Specifically, the quantum measurement control unit 12 controls the first quantum computer 20 to:

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[0051] Here, A = I (identity operator) or A = ρ. In the power subspace method, σ i =ρ i In the prior art, σ i In the conventional method, only the Pauli operator is used, and the quantum errors that can be removed are limited to coherent errors. In this embodiment, quantum errors other than coherent errors can be suppressed. i ρ i and the Pauli operator, which allows for efficient suppression of coherent errors.

[0052] The error suppression calculation unit 13 calculates the error suppression (step S103). Specifically, the error suppression calculation unit 13 calculates the generalized characteristic equation

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[0054] Next, the quantum error suppression unit 14 calculates the physical quantity in which the error is suppressed (step S104).

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[0057] For example, when a physical quantity O measurable by the quantum measurement circuit 31 is given, the expected value of the physical quantity O with quantum errors suppressed is

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[0062] According to this embodiment, by applying the power subspace method to calculate error suppression, an ideal quantum state can be expressed as a series expansion of a quantum state that has been subjected to a quantum error, thereby achieving higher calculation accuracy than the virtual distillation method, etc., in which accuracy is limited by the number of copies of the quantum state. Therefore, it is possible to improve the performance of quantum error suppression compared to conventional techniques.

[0063] Example 2 In this embodiment, an example of suppressing quantum errors by applying the "error subspace method" as a generalized subspace expansion method will be described. The following mainly describes the differences from the first embodiment.

[0064] The quantum measurement circuit 23 according to this embodiment is a quantum circuit for performing measurements on quantum entanglement of a plurality of quantum states by applying the "error subspace method."

[0065] In the quantum measurement process according to this embodiment, in step S102 of Fig. 6, the quantum measurement control unit 12 controls the first quantum computer 20 to perform measurement using the "error subspace method." The "error subspace method" is a method that can expand the range of expressible quantum states by using quantum states with amplified errors, and can incorporate the effect of quantum error suppression, known as the extrapolation method of the prior art, and is a method that can improve calculation accuracy.

[0066] Specifically, the quantum measurement control unit 12 controls the first quantum computer 20 to calculate a matrix representing a Hamiltonian on the subspace and an overlap matrix of the subspace, similar to Example 1. Here, A=I (identity operator), and σ i =ρ(λ i ε), where λ i >1,ε is a parameter that represents the magnitude of the quantum error in the quantum state. Also, σ i ρ(λ iε) and the Pauli operator, which allows for efficient suppression of coherent errors.

[0067] According to this embodiment, by applying the error subspace method to calculate error suppression and using a quantum state with increased calculation error, error suppression that incorporates the advantages of the extrapolation method of the quantum error suppression method can be realized, and higher calculation accuracy can be achieved than with methods such as virtual distillation, in which accuracy is limited by the number of copies of the quantum state. Therefore, it is possible to improve the performance of quantum error suppression compared to conventional techniques.

[0068] (Addendum) The following additional clauses are disclosed in relation to the above-described embodiment. (Additional note 1) Memory and at least one processor coupled to the memory, The processor: Calculating multiple quantum states including a quantum state affected by the quantum error to be suppressed; measuring a matrix representing a Hamiltonian on a subspace defined by a positive semidefinite operator associated with the plurality of quantum states and an overlap matrix of the subspace, with the positive semidefinite operator being the identity operator or a quantum state affected by the quantum error; calculating an eigenenergy of the Hamiltonian in which the quantum error has been suppressed as an eigenvalue of a generalized eigenequation representing the Hamiltonian; calculating an expectation value of a physical quantity from the physical quantity that is the object of quantum measurement based on the calculated eigenenergy of the Hamiltonian; Control device. (Additional note 2) the processor determines a matrix representing a Hamiltonian on the subspace and an overlap matrix of the subspace using a power subspace method; Item 1. The control device according to claim 1. (Additional note 3) The processor measures a matrix representing a Hamiltonian on the subspace and an overlap matrix of the subspace using an error subspace method. Item 1. The control device according to claim 1. (Additional note 4) 1. A quantum measurement system comprising a controller, a first quantum computer, and a second quantum computer, The control device Memory and at least one processor coupled to the memory; The processor: Calculating multiple quantum states including a quantum state affected by the quantum error to be suppressed; measuring a matrix representing a Hamiltonian on a subspace defined by a positive semidefinite operator associated with the plurality of quantum states and an overlap matrix of the subspace, with the positive semidefinite operator being the identity operator or the quantum state affected by the quantum error; calculating an eigenenergy of the Hamiltonian in which the quantum error has been suppressed as an eigenvalue of a generalized eigenequation representing the Hamiltonian; calculating an expectation value of a physical quantity from the physical quantity that is the object of quantum measurement based on the calculated eigenenergy of the Hamiltonian; Quantum measurement systems. (Additional note 5) A computer-implemented control method comprising: Calculating multiple quantum states including a quantum state affected by the quantum error to be suppressed; measuring a matrix representing a Hamiltonian on a subspace defined by a positive semidefinite operator associated with the plurality of quantum states and an overlap matrix of the subspace, with the positive semidefinite operator being the identity operator or the quantum state affected by the quantum error; calculating an eigenenergy of the Hamiltonian in which the quantum error has been suppressed as an eigenvalue of a generalized eigenequation representing the Hamiltonian; calculating an expectation value of a physical quantity from the physical quantity that is the object of quantum measurement based on the calculated eigenenergy of the Hamiltonian; Control method. (Additional note 6) A non-transitory storage medium storing a program for causing a computer to function as each unit in the control device described in any one of appendixes 1 to 3.

[0069] Although the present embodiment has been described above, the present invention is not limited to such a specific embodiment, and various modifications and changes are possible within the scope of the gist of the present invention described in the claims. [Explanation of symbols]

[0070] 1. Quantum Measurement System 10 Control device 11 Quantum state calculation unit 12 Quantum measurement control section 13 Error suppression calculation unit 14 Quantum Error Suppression Unit 20. The First Quantum Computer 21 First quantum circuit 22 Second quantum circuit 23 Quantum measurement circuit 30 Second quantum computer 31 Quantum measurement circuit 40,50 communication lines 500 computers 501 Input Device 502 Display device 503 External I / F 503a Recording media 504 Communication I / F 505 processor 506 Memory Device 507 Bus

Claims

1. a quantum state calculation unit that calculates a plurality of quantum states including a quantum state affected by a quantum error to be suppressed; a quantum measurement control unit that measures a matrix representing a Hamiltonian on a subspace defined by a semidefinite operator associated with the plurality of quantum states and an overlap matrix of the subspace, with the semidefinite operator being an identity operator or a quantum state affected by the quantum error; an error suppression calculation unit that calculates an eigenenergy of the Hamiltonian in which the quantum error is suppressed as an eigenvalue of a generalized eigenequation that represents the Hamiltonian; a quantum error suppression unit that calculates an expected value of a physical quantity from a physical quantity that is a target of quantum measurement based on the calculated eigenenergy of the Hamiltonian, The quantum measurement control unit measures a matrix representing a Hamiltonian on the subspace and an overlap matrix of the subspace using a power subspace method or an error subspace method. Control device.

2. 1. A quantum measurement system comprising a controller, a first quantum computer, and a second quantum computer, The control device a quantum state calculation unit that calculates, using the first quantum computer, a plurality of quantum states including a quantum state affected by a quantum error to be suppressed; a quantum measurement control unit that uses the first quantum computer to measure a matrix representing a Hamiltonian on a subspace defined by a semidefinite operator associated with the plurality of quantum states and an overlap matrix of the subspace, with the semidefinite operator being an identity operator or a quantum state affected by the quantum error; an error suppression calculation unit that calculates an eigenenergy of the Hamiltonian in which the quantum error is suppressed as an eigenvalue of a generalized eigenequation that represents the Hamiltonian; a quantum error suppression unit that calculates an expected value of a physical quantity from a physical quantity measured using the second quantum computer based on the calculated eigenenergy of the Hamiltonian, The quantum measurement control unit measures a matrix representing a Hamiltonian on the subspace and an overlap matrix of the subspace using a power subspace method or an error subspace method. Quantum measurement systems.

3. A computer-implemented control method comprising: calculating a plurality of quantum states including a quantum state affected by a quantum error to be suppressed; a step of measuring a matrix representing a Hamiltonian on a subspace defined by a positive semidefinite operator associated with the plurality of quantum states and an overlap matrix of the subspace, the positive semidefinite operator being an identity operator or a quantum state affected by the quantum error; calculating an eigenenergy of the Hamiltonian in which the quantum error has been suppressed as an eigenvalue of a generalized eigenequation representing the Hamiltonian; and calculating an expectation value of the physical quantity from the physical quantity that is the object of quantum measurement based on the calculated eigenenergy of the Hamiltonian; the measuring step measures a matrix representing a Hamiltonian on the subspace and an overlap matrix of the subspace using a power subspace method or an error subspace method; Control method.

4. A program for causing a computer to function as each unit in the control device according to claim 1.

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